Problem: Simplify the following expression: $a = \dfrac{10}{x - 2} \div \dfrac{4}{8x}$
Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{10}{x - 2} \times \dfrac{8x}{4}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 10 \times 8x } { (x - 2) \times 4}$ $a = \dfrac{80x}{4x - 8}$ Simplify: $a = \dfrac{20x}{x - 2}$